While some of this has some basis in truth, most of it doesn't. I addressed a number of myths about the Middle Ages, in another essay.
In any event, we hardly think of medieval times as a period of intellectual growth. And indeed, it does seem difficult to believe that in a time when war & famine, drought & pestilence threatened everyone, and survival was difficult even for some of the well-to-do, that the Middle Ages could have been a time of intellectual innovation.
But the fact remains, that it was a time of philosophical advance & a growing realization that intellectual pursuits were important & worthy pastimes.
There was an unspoken "ideal" of a Churchman as a literate, learned thinker. The inspiration for this ideal were the "Church Fathers," such as St. Augustine and St. Jerome, of classical times. While many clergy failed to live up to this ideal, it nonetheless inspired many to educate themselves, and teach others.
All Benedictines were expected to be literate and well-read, not only in Scripture, but in the writings of the Church Fathers & even some of the assorted other Roman classics. (The Greek classics were not discovered until later in the Middle Ages, & never had the same kind of revered status, at least during medieval times.)
Eventually, these scholars would break up into other colleges, and as some of the early collegians grew older, they would found new colleges with younger scholars. There, the older collegians would teach, or even lecture, in addition to orchestrating seminars or debates. Many colleges stuck to particular topics, such as theology, or metaphysics, or mathematics & geometry. Others reached out to embrace all topics, & these became known as "universities."
Colleges tended to aggregate in certain areas, where students sometimes went from one, to another, & back again. This was certainly true of Paris, the magnet of intellectualism during the Middle Ages. Its universities and colleges, & hence their students, were considered the best & brightest of all.
Outside of western Europe, there were some other areas which were intellectual magnets, of their own. Toledo in Spain became a center of Judaic learning; Granada, Spain became a center for Islamic knowledge; and Alexandria and Constaninople became centers of learning for the Orthodox Church.
Not all the students at the colleges and universities became clergy, however, many did, and some of the colleges were essentially Benedictine schools. They attracted only the very brightest students, & just being admitted to one was a great honor.
One of the more outstanding examples of this was St. Anselm's "ontological proof" of the existence of God. The very idea of proving God's existence had been all but forbidden — to prove his existence, implied that he might not, & therefore any such proof must, by definition, be profane! In order to save space in this essay, I'll explain Anselm's proof in another essay; read it, if you wish to learn about it.
Indeed, Anselm, a student of the Paris colleges who'd become Archbishop of Canterbury in England, was briefly excommunicated, for having published this. (He released this proof quite some time after having come up with it, showing his awareness of the ramifications & his reluctance to have to face them.) He was able to justify himself, ultimately, in this way: Assuming God exists, there must be a way logically to demonstrate this; if one could do so, it would prove the veracity and practicality of the discipline of logic, and might also lead one to corollary truths. In other words, Anselm was claiming not to imply that God might not exist, but that logic might instead be fallible — by using it to prove a "known" proposition — i.e. that God exists — he could show the usefulness of logic.
Anselm's proof, by the way, was flawed. (See my essay on the topic to find out why.) Nevertheless, Anselm's release of his "proof," and the Church's grudging acceptance of it, was part of a larger change in thought which was going on, at that time.
Mathematics was virtually reborn, with the return of the Greek classics (Aristotle & Euclid, mainly) and the introduction of the Arabic numerals, which had a symbol for zero. While classical Roman mathematics had been based upon the Greek, & had been quite advanced in its own right, the lack of a numeral for zero had placed tremendous limits upon it. Those limits were cast off, however, and mathematics began to grow.
Similarly, other avenues of thought opened up, which had previously been limited. Metaphysics became even more introspective; medieval collegians debated such questions as how many angels could dance on the head of a pin. Platonic realism and Aristotlean nominalism were debated at length. The scope of theology widened, as collegians attempted to understand the very nature of God.
These pursuits continued on into the Renaissance, eventually becoming the foundation for modern science. The so-called "scientific method" of hypothesis, test-by-experimentation, amend hypothesis, test-new-hypothesis, etc. comes down to us from the works of Roger Bacon, an English monk. We have these medieval collegians to thank for modern science & all the technology we enjoy, today.
River-mills as we know them were a medieval invention. They were originally used to turn huge grinding-wheels to pulverize grain into flour, but soon were also used to operate spindles used to make thread and/or rope. Exactly when and where they were invented is uncertain, however, the Cistercian monastic order built a great many mills & developed many improvements on their design. By the end of the Middle Ages, nearly every village had a mill operating — since almost every village stood along a river.
Refinements to agricultural techniques — such as allowing fields to lie fallow, the breeding (through cross-pollination) of more productive forms of crops, improved plow design to till the soil more deeply & extract rocks which hindered crops, & improved irrigation techniques — all took place over a long period of time, and eventually made the medieval farmer more productive. This increase in productivity on farms allowed the towns to grow, which in turn fueled an increase in commerce and industry.
Thus, by the end of the Middle Ages, the towns had grown in both commercial and political power, and began to eclipse the old order (the feudal system, based on an agrarian economy, with the farm/manor as its core). Over the next couple of centuries, this change would lead to the end of the feudal system and hence give birth to the Industrial Age.
All of these technological changes were painfully slow in coming, however, taking generations to develop to fruition. These days, technology changes immensely in a matter of months; in the Middle Ages, it took decades, & sometimes even centuries. There were a great many reasons why it took so long for changes to take place, among them:
The "scientific method," as mentioned above, originated in the Middle Ages, & gave us modern medicine and science. Algebra, the basis of modern mathematics, was born during the Middle Ages, among Moslem scholars.
Most of the social sciences — particularly history — also were "born" in the Middle Ages. Events had been chronicled since ancient times — beginning with Herodotus centuries BCE — but it was medieval collegians who thought to examine events & determine their greater meaning & future implications.